A Systematic Approach for Constructing Higher-Order Embedded Boundary Methods and Its Application to Inviscid Compressible Flow in Fluid-Structure Interactions

Xianyi Zeng
Seminar

A systematic approach is presented for constructing higher-order embedded boundary methods for solving partial differential equations (PDE) with dynamic boundary conditions in general, and fluid-structure interaction (FSI) problems in particular. Such methods are gaining popularity because they simplify a number of computational issues. These range from gridding the fluid domain, to designing Eulerian-based algorithms for challenging fluid structure applications characterized by large structural motions and deformations. However, because they typically operate on non body-fitted meshes, embedded boundary methods also complicated other issues such as treatment of wall boundary conditions in general, and fluid-structure transmission condition in particular. These methods also tend to be at best first-order space-accurate at the embedded boundaries; and in some cases they are provably inconsistent at these locations.

To address this issue, the proposed methodology leads to a departure from the current practice of populating ghost fluid values independently from the chosen spatial discretization scheme. Instead, it accounts for the pattern and properties of a preferred higher-order discretization scheme, and attributes ghost values as to preserve the formal order of spatial accuracy of this scheme. The methodology is described with assumption of prescribed moving wall boundary conditions, however its extension to flow-induced structural motions is straightforward. It is illustrated by its application to various finite difference and finite volume methods. Its impact is also demonstrated by multi-dimensional numerical experiments that confirm its theoretically proven ability to preserve higher-order spatial accuracy, including in the vicinity of the embedded interfaces.